Department of Systems Science, School of Management and Center for Complexity Research, Beijing Normal University, Beijing, People's Republic of China.
PLoS One. 2011;6(11):e27418. doi: 10.1371/journal.pone.0027418. Epub 2011 Nov 14.
Many complex systems can be represented as networks, and how a network breaks up into subnetworks or communities is of wide interest. However, the development of a method to detect nodes important to communities that is both fast and accurate is a very challenging and open problem.
METHODOLOGY/PRINCIPAL FINDINGS: In this manuscript, we introduce a new approach to characterize the node importance to communities. First, a centrality metric is proposed to measure the importance of network nodes to community structure using the spectrum of the adjacency matrix. We define the node importance to communities as the relative change in the eigenvalues of the network adjacency matrix upon their removal. Second, we also propose an index to distinguish two kinds of important nodes in communities, i.e., "community core" and "bridge".
CONCLUSIONS/SIGNIFICANCE: Our indices are only relied on the spectrum of the graph matrix. They are applied in many artificial networks as well as many real-world networks. This new methodology gives us a basic approach to solve this challenging problem and provides a realistic result.
许多复杂系统都可以表示为网络，网络如何分解成子网络或社区是一个广泛关注的问题。然而，开发一种快速而准确的检测对社区重要的节点的方法是一个极具挑战性和开放性的问题。
方法/主要发现：在本文中，我们引入了一种新的方法来描述节点对社区的重要性。首先，提出了一种基于邻接矩阵谱的中心性度量方法，用于衡量网络节点对社区结构的重要性。我们将节点对社区的重要性定义为网络邻接矩阵特征值在节点移除前后的相对变化。其次，我们还提出了一种指标来区分社区中的两种重要节点，即“社区核心”和“桥”。
结论/意义：我们的指标仅依赖于图矩阵的谱。它们被应用于许多人工网络和许多真实世界的网络。这种新的方法为我们解决这个具有挑战性的问题提供了一个基本的方法，并给出了一个现实的结果。
